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High-frequency digital oscilloscopes are often prone to systematic errors in sampling time or time base distortion (TBD). This error greatly affects the quality of the acquisition of fast signals, but its systematic nature makes measurement and correction possible and greatly advantageous. Existing techniques for measuring TBD exhibit good performance with equivalent-time sampling digitizers, but they are not able to measure the distortion in real-time analog-memory systems - a technology of widespread use in modern gigasamples/second sampling scopes. This paper illustrates the correct measurement technique that was developed according to the hardware peculiarities of analog-memory sampling digitizers. The performance of the developed techniques are theoretically evaluated and practically demonstrated in the experimental characterization of an actual real-time analog-memory scope.